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Jobisdone [24]
3 years ago
6

The length of rectangular field is 7 m less than 4 times the width. The perimeter is 136 m. Find the width and length

Mathematics
2 answers:
iris [78.8K]3 years ago
5 0

Answer:

15 m and 53 m.

Step-by-step explanation:

Let the length of the rectangular field = x m

and width = y m

From the statement "Length is 7m less than 4 times the width"

x = 4y - 7 ----------(1)

"perimeter of the field is 136 m."

2 (x + y) = 136

x + y = 68 ---------(2)

Now we replace the value of x from equation 1 to 2

4y - 7 + y = 68

5y - 7 = 68

5y = 68 + 7 = 75

y = 15 m

From equation (2)

x + 15 = 68

x = 68 - 15

  = 53 m

Therefore, length and width of the field are 15 m and 53 m.

Elena-2011 [213]3 years ago
3 0
P = 2(L + W)
P = 136
L = 4W - 7

136 = 2(4W - 7 + W)
136 = 2(5W - 7)
136 = 10W - 14
136 + 14 = 10W
150 = 10W
150/10 = W
15 = W <=== width is 15 m

L = 4W - 7
L = 4(15) - 7
L = 60 - 7
L = 53 <== length is 53 m
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Step-by-step explanation:

Let's assume this is a number line were given.

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Length of ST = the difference between T and S

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A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm. what is the approximate area
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The area of the regular heptagon which has a radius of approximately 27.87 cm and the length of each side is 24.18 cm is 2125 cm².

<h3>What is the area of a heptagon?</h3>

Heptagon is the closed shape polygon which has 7 sides and 7 interior angles.

The area of the regular heptagon is found out using the following formula.

A=\dfrac{7a}{4}\cot \left(\dfrac{180}{7}\right)

Here, (<em>a</em>) is the length of the heptagon.

A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm. Put the value of side in the above formula,

A=\dfrac{7\times24.18}{4}\cot \left(\dfrac{180}{7}\right)\\A\approx 2125\rm\; cm^2

Hence, the area of the regular heptagon which has a radius of approximately 27.87 cm and the length of each side is 24.18 cm is 2125 cm².

Learn more about the area of a heptagon here;

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10. 10. If AB bisects CAF, and m&lt;EAF = 72°,<br>then the m&lt;BAF =​
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The measure of ∠BAF is 54°.

Solution:

DF and CE are intersecting lines.

m∠EAF = 72° and AB bisects ∠CAF.

∠EAF and ∠DAC are vertically opposite angles.

Vertical angle theorem:

<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>

∠DAC ≅ ∠EAF

m∠DAC = 72°

<em>Sum of the adjacent angles in a straight line = 180°</em>

m∠DAE + m∠EAF = 180°

m∠DAE + 72° = 180°

Subtract 72° from both sides.

m∠DAE = 108°

∠CAF and ∠DAE are vertically opposite angles.

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AB bisects ∠CAF means ∠CAB = ∠BAF

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m∠BAF + m∠BAF = 108°

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Divide by 2 on both sides, we get

m∠BAF = 54°

Hence the measure of ∠BAF is 54°.

4 0
3 years ago
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